Question: Divide. Write the quotient in lowest terms. $\dfrac{1}{4} \div 1\dfrac1{8} = $
First, let's rewrite $1\dfrac1{8}$ as a fraction: $\dfrac{1}{4} \div 1\dfrac1{8} =\dfrac{1}{4} \div \dfrac{9}{8}$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac98$ is $\dfrac8{9}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{1}{4} \div \dfrac{9}{8}=\dfrac{1}{4}\times\dfrac8{9}$ $=\dfrac{1\times 8}{4\times 9}$ $=\dfrac{ 1 \times~\stackrel{2}{\cancel{ 8 }}}{\underset{1}{\cancel 4\times9}} $ $=\dfrac{1\times 2}{1\times 9}$ $=\dfrac{2}{9}$